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Use Green’s Theorem to evaluate (Check the orientation of the curve before applying the theorem.)

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Use Green’s Theorem to evaluate (Check the orientation of the curve before applying the theorem.)

asked Feb 18, 2015 in CALCULUS by anonymous
reshown Feb 18, 2015 by goushi

1 Answer

0 votes

Step 1:

The vector field is .

Green's theorem :

If C  be a positively oriented closed curve, and R be the region bounded by C, M  and N  are the partial derivatives on an open region then

image

Green's theorem can be applied because is a closed curve, but the theorem is applicable for positively oriented curves.

This curve rotates in a clockwise direction, so negative should be added before a integral.

image

Using polar coordinates, image and circle radius is 2.

So image

                 image

image.

Solution :

image.

answered Feb 21, 2015 by joseph Apprentice

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